Crash-Neutral Currency Carry Trades Jakub W. Jurek Princeton - - PowerPoint PPT Presentation

Crash-Neutral Currency Carry Trades

Jakub W. Jurek

Princeton University – Bendheim Center for Finance

March 2009

Currency Carry Trade

Currency carry trades exploit violations of uncovered interest parity (UIP) by buying (selling) currencies with relatively high (low) interest rates.

Currency Carry Trade

Historical returns:

◮ Before (USD/G10; monthly, 1990:1-2007:03)

RMRF SMB HML UMD FX Carry Mean 0.0730 0.0227 0.0477 0.0985 0.0478 t-stat 2.13 0.75 1.72 2.51 3.91

• St. dev.

0.1422 0.1261 0.1153 0.1630 0.0507 Skewness

• 0.68

0.81 0.11

• 0.66
• 0.95

SR 0.51 0.18 0.41 0.60 0.94

Currency Carry Trade

Historical returns:

◮ Before (USD/G10; monthly, 1990:1-2007:03)

RMRF SMB HML UMD FX Carry Mean 0.0730 0.0227 0.0477 0.0985 0.0478 t-stat 2.13 0.75 1.72 2.51 3.91

• St. dev.

0.1422 0.1261 0.1153 0.1630 0.0507 Skewness

• 0.68

0.81 0.11

• 0.66
• 0.95

SR 0.51 0.18 0.41 0.60 0.94

◮ After (USD/G10; monthly, 1990:1-2008:10)

RMRF SMB HML UMD FX Carry Mean 0.0477 0.0191 0.0392 0.1060 0.0331 t-stat 1.39 0.68 1.50 2.83 2.55

• St. dev.

0.1485 0.1223 0.1136 0.1628 0.0563 Skewness

• 0.84

0.83 0.11

• 0.60
• 1.63

SR 0.32 0.16 0.35 0.65 0.59

Paper Summary

This paper tests the hypothesis that violations of UIP are attributable to crash risk premia by examining data on foreign exchange options:

• 1. Dynamics of risk-neutral skewness:

◮ Negatively related to contemporaneous interest rate differential in the cross-section;

weak time-series relation.

◮ Does not forecast currency excess returns. ◮ Moves opposite to future realized skewness in response to realized currency moves.

Paper Summary

This paper tests the hypothesis that violations of UIP are attributable to crash risk premia by examining data on foreign exchange options:

• 1. Dynamics of risk-neutral skewness:

◮ Negatively related to contemporaneous interest rate differential in the cross-section;

weak time-series relation.

◮ Does not forecast currency excess returns. ◮ Moves opposite to future realized skewness in response to realized currency moves.

• 2. Crash-neutral currency carry trades:

◮ Returns smaller than for standard carry trades, but positive and statistically significant. ◮ Results robust to inclusion of transaction costs. ◮ Crash-based explanation would requires option implied volatilities that are 2-4x the

actual values observed in the data.

Uncovered Interest Parity

◮ Uncovered interest parity (UIP) predicts that high interest currencies should

depreciate relative to low interest rate currencies, such that investors are indifferent between holding deposits in the two.

◮ St – spot exchange rate (price of foreign currency in USD) ◮ Ft,τ – forward exchange rate

Ft,τ = St · exp ((rd,t − rf ,t) · τ)

Uncovered Interest Parity

◮ Uncovered interest parity (UIP) predicts that high interest currencies should

depreciate relative to low interest rate currencies, such that investors are indifferent between holding deposits in the two.

◮ St – spot exchange rate (price of foreign currency in USD) ◮ Ft,τ – forward exchange rate

Ft,τ = St · exp ((rd,t − rf ,t) · τ)

◮ Following Hansen and Hodrick (1989), UIP is typically tested by running a

regression of the log currency return on the log forward spread: st+1 − st = a0 + a1 · (ft − st) + εt+1 = a0 + a1 · (rd,t − rf ,t) · τ + εt+1

◮ Null hypothesis (H0): a0 = 0 and a1 = 1.

Uncovered Interest Parity

Testing UIP in the panel of G10 currencies (Table I)

The intercept of the UIP regression is negative for 6 of 9 countries in the full sample (1990-2007) and in all countries during the 1999-2007 sample.

1990-2007 1999-2007 Currency ˆ a0 ˆ a1 R2 NFE χ2 test ˆ a0 ˆ a1 R2 NFE χ2 test AUD

• 0.0025
• 1.7483

0.0105 8.87

• 0.0028
• 3.9018

0.0310 9.34 (0.0023) (1.0522) (0.01) (0.0036) (1.9520) (0.01) CAD

• 0.0001
• 0.5077

0.0019 9.13 0.0027

• 2.5012

0.0115 5.06 (0.0009) (0.5104) (0.01) (0.0015) (2.1091) (0.08) CHF 0.0026

• 1.2815

0.0069 5.60 0.0096

• 4.5238

0.0350 9.03 (0.0024) (1.0008) (0.06) (0.0041) (1.8485) (0.01) EUR 0.0002

• 0.0320
• 0.0002

1.34 0.0036

• 4.4836

0.0447 11.19 (0.0016) (0.9072) (0.51) (0.0024) (1.6590) (0.00) GBP 0.0021 0.7061 0.0020 3.65 0.0001

• 1.7371

0.0061 4.55 (0.0019) (1.2755) (0.16) (0.0025) (1.7738) (0.10) JPY 0.0058

• 2.0823

0.0165 12.33 0.0048

• 1.8183

0.0099 6.20 (0.0025) (0.8787) (0.00) (0.0045) (1.4003) (0.05) NOK 0.0013 0.6255 0.0042 1.43 0.0007

• 1.4005

0.0090 5.46 (0.0017) (0.6351) (0.49) (0.0026) (1.2175) (0.07) NZD

• 0.0047
• 2.4128

0.0147 15.46

• 0.0067
• 4.7728

0.0482 17.15 (0.0034) (1.1975) (0.00) (0.0045) (1.6837) (0.00) SEK 0.0004 0.6081 0.0046 0.51 0.0026

• 3.5247

0.0405 11.09 (0.0017) (0.6046) (0.77) (0.0024) (1.3764) (0.00) Pooled FE

• 0.1795

0.0002 2.59 FE

• 3.0503

0.0248 24.17 (0.6589) (0.99) (1.1190) (0.01) XS 0.0005

• 0.1883

0.1070

• 0.0012
• 0.5994

0.0966

• (0.0003)

(0.0836) (0.0005) (0.1087)

Uncovered Interest Parity

Testing UIP in the panel of G10 currencies (Table I)

At the 10% significance level, UIP is rejected in 5 of 9 countries in the full sample (1990-2007) and in all countries during the 1999-2007 sample.

1990-2007 1999-2007 Currency ˆ a0 ˆ a1 R2 NFE χ2 test ˆ a0 ˆ a1 R2 NFE χ2 test AUD

• 0.0025
• 1.7483

0.0105 8.87

• 0.0028
• 3.9018

0.0310 9.34 (0.0023) (1.0522) (0.01) (0.0036) (1.9520) (0.01) CAD

• 0.0001
• 0.5077

0.0019 9.13 0.0027

• 2.5012

0.0115 5.06 (0.0009) (0.5104) (0.01) (0.0015) (2.1091) (0.08) CHF 0.0026

• 1.2815

0.0069 5.60 0.0096

• 4.5238

0.0350 9.03 (0.0024) (1.0008) (0.06) (0.0041) (1.8485) (0.01) EUR 0.0002

• 0.0320
• 0.0002

1.34 0.0036

• 4.4836

0.0447 11.19 (0.0016) (0.9072) (0.51) (0.0024) (1.6590) (0.00) GBP 0.0021 0.7061 0.0020 3.65 0.0001

• 1.7371

0.0061 4.55 (0.0019) (1.2755) (0.16) (0.0025) (1.7738) (0.10) JPY 0.0058

• 2.0823

0.0165 12.33 0.0048

• 1.8183

0.0099 6.20 (0.0025) (0.8787) (0.00) (0.0045) (1.4003) (0.05) NOK 0.0013 0.6255 0.0042 1.43 0.0007

• 1.4005

0.0090 5.46 (0.0017) (0.6351) (0.49) (0.0026) (1.2175) (0.07) NZD

• 0.0047
• 2.4128

0.0147 15.46

• 0.0067
• 4.7728

0.0482 17.15 (0.0034) (1.1975) (0.00) (0.0045) (1.6837) (0.00) SEK 0.0004 0.6081 0.0046 0.51 0.0026

• 3.5247

0.0405 11.09 (0.0017) (0.6046) (0.77) (0.0024) (1.3764) (0.00) Pooled FE

• 0.1795

0.0002 2.59 FE

• 3.0503

0.0248 24.17 (0.6589) (0.99) (1.1190) (0.01) XS 0.0005

• 0.1883

0.1070

• 0.0012
• 0.5994

0.0966

• (0.0003)

(0.0836) (0.0005) (0.1087)

Currency Carry Trade

The currency carry trade exploits deviations from UIP by borrowing funds in currencies with low interest rates and investing them in currencies with high interest rates.

◮ Investor constructs carry trades in X/USD currency pairs (X ∈ G10) ◮ Funds are borrowed/invested at the relevant one-month LIBOR rates. ◮ Positions are held for one month. ◮ Payoffs:

• CT t+1 =

rf ,t > rd,t : exp

• rf ,t · τ
• · ˜

St+τ − exp

• rd,t · τ
• · St

rd,t > rf ,t : exp

• rd,t · τ
• · St − exp
• rf ,t · τ
• · ˜

St+τ

Currency Carry Trade

Portfolio strategies

Consider the following portfolio formation rules:

• 1. Equal-weighted (EQL)
• 2. Spread-weighted (SPR)
• 3. Equal-weighted dollar-neutral (EQL-$N)
• 4. Spread-weighted dollar-neutral (SPR-$N)

Portfolio USD Exposure Currency rf ,t − rd,t EQL SPR AUD 1.88%

• 0.11
• 0.14

CAD 0.05%

• 0.11
• 0.00

GBP 1.28%

• 0.11
• 0.09

NOK 1.29%

• 0.11
• 0.09

NZD 2.78%

• 0.11
• 0.20

CHF

• 2.11%

0.11 0.15 EUR

• 0.42%

0.11 0.03 JPY

• 3.45%

0.11 0.25 SEK

• 0.32%

0.11 0.02 Net USD

• 0.11
• 0.07

Currency Carry Trade

Portfolio strategies

Consider the following portfolio formation rules:

• 1. Equal-weighted (EQL)
• 2. Spread-weighted (SPR)
• 3. Equal-weighted dollar-neutral (EQL-$N)
• 4. Spread-weighted dollar-neutral (SPR-$N)

Portfolio USD Exposure Currency rf ,t − rd,t EQL SPR EQL-$N SPR-$N AUD 1.88%

• 0.11
• 0.14
• 0.20
• 0.26

CAD 0.05%

• 0.11
• 0.00
• 0.20
• 0.01

GBP 1.28%

• 0.11
• 0.09
• 0.20
• 0.18

NOK 1.29%

• 0.11
• 0.09
• 0.20
• 0.18

NZD 2.78%

• 0.11
• 0.20
• 0.20
• 0.38

CHF

• 2.11%

0.11 0.15 0.25 0.33 EUR

• 0.42%

0.11 0.03 0.25 0.07 JPY

• 3.45%

0.11 0.25 0.25 0.55 SEK

• 0.32%

0.11 0.02 0.25 0.05 Net USD

• 0.11
• 0.07

0.00 0.00

Currency Carry Trade

Historical performance (Figure 1)

Simple portfolio construction rules (e.g. equal- and spread-weighting) were close to being ex post efficient.

Currency Carry Trade

Historical performance – portfolio strategies (Table II)

1999:1-2007:3 (N = 99) EQL SPR EQL-$N SPR-$N Mean 0.0560 0.0844 0.0434 0.0699 t-stat 3.63 4.26 2.30 2.84

• Std. dev.

0.0443 0.0569 0.0543 0.0707 Skewness

• 0.42
• 0.20
• 0.52
• 0.23

Kurtosis 3.73 2.97 4.31 4.33 Min

• 0.0368
• 0.0335
• 0.0569
• 0.0661

Max 0.0375 0.0455 0.0369 0.0651 Carry 0.0200 0.0307 0.0345 0.0478 SR 1.26 1.48 0.80 0.99

Currency Carry Trade

Historical performance – portfolio strategies (Table II)

1999:1-2007:3 (N = 99) EQL SPR EQL-$N SPR-$N Mean 0.0560 0.0844 0.0434 0.0699 t-stat 3.63 4.26 2.30 2.84

• Std. dev.

0.0443 0.0569 0.0543 0.0707 Skewness

• 0.42
• 0.20
• 0.52
• 0.23

Kurtosis 3.73 2.97 4.31 4.33 Min

• 0.0368
• 0.0335
• 0.0569
• 0.0661

Max 0.0375 0.0455 0.0369 0.0651 Carry 0.0200 0.0307 0.0345 0.0478 SR 1.26 1.48 0.80 0.99 1999:1-2008:10 (N = 117) EQL SPR EQL-$N SPR-$N Mean 0.0266 0.0482 0.0119 0.0291 t-stat 1.46 2.10 0.48 0.90

• Std. dev.

0.0568 0.0717 0.0778 0.1014 Skewness

• 2.08
• 1.68
• 2.29
• 2.06

Kurtosis 12.95 10.00 14.11 12.66 Min

• 0.0958
• 0.1098
• 0.1360
• 0.0651

Max 0.0375 0.0455 0.0369 0.0651 Carry 0.0202 0.0310 0.0352 0.0491 SR 0.47 0.67 0.15 0.29

Currency Carry Trade

Net USD Exposure (1999:1-2008:10)

The net exposure to USD is driven primarily by aggressive U.S. monetary policy.

Currency Carry Trade

Historical performance decomposition

◮ Equal-weighted (EQL)

1999:1-2007:03 2007:4-2008:10 Total Long Short Total Long Short Mean 0.0560 0.0136 0.0424

• 0.1349
• 0.0428
• 0.0921

t-stat 3.88 0.97 3.10

• 1.85
• 1.66
• 1.20
• Std. dev.

0.0443 0.0433 0.0419 0.0894 0.0316 0.0942 Skewness

• 0.43
• 0.33

0.83

• 2.29
• 1.54
• 1.96

Currency Carry Trade

Historical performance decomposition

◮ Equal-weighted (EQL)

1999:1-2007:03 2007:4-2008:10 Total Long Short Total Long Short Mean 0.0560 0.0136 0.0424

• 0.1349
• 0.0428
• 0.0921

t-stat 3.88 0.97 3.10

• 1.85
• 1.66
• 1.20
• Std. dev.

0.0443 0.0433 0.0419 0.0894 0.0316 0.0942 Skewness

• 0.43
• 0.33

0.83

• 2.29
• 1.54
• 1.96

◮ Equal-weighted dollar-neutral (EQL-$N)

1999:1-2007:03 2007:4-2008:10 Total Long Short Total Long Short Mean 0.0435

• 0.0013

0.0448

• 0.1633
• 0.0656
• 0.0977

t-stat 2.46

• 0.05

1.73

• 1.41
• 0.94
• 0.86
• Std. dev.

0.0543 0.0746 0.0793 0.1417 0.0855 0.1399 Skewness

• 0.53
• 0.46
• 0.01
• 1.56

0.24

• 1.09

Crash Risk

Related literature

Recent research on currencies borrows from the equity literature and focuses on the role of crash risk:

◮ Equities: Rietz (1988), Barro (2006), Weitzman (2007) ◮ Equity options: Coval and Shumway (2001), Pan (2002), Bakshi and Kapadia

(2003), and Driessen and Maenhout (2006)

◮ Currencies: Brunnermeier, Nagel and Pedersen (2008), Farhi and Gabaix (2008),

Plantin and Shin (2008) Ongoing debate regarding whether classical asset pricing models can rationalize excess returns to the currency carry trade.

◮ No: Burnside (2007), Burnside, et al. (2008) ◮ Yes: Verdelhan and Lustig (2006, 2007), Verdelhan (2008), Lustig, Roussanov

and Verdelhan (2008)

Foreign Exchange Options

Data

Data:

◮ European OTC options on X/USD exchange rates (source: J. P. Morgan) ◮ Cross section: X = AUD, CAD, CHF, GBP, EUR, JPY, NOK, NZD, SEK ◮ Time series: 1999:1 - 2008:10 ◮ Strikes: 10δp, 25δp, ATM, 25δc, 10δc ◮ Tenors: 1M, 3M, 6M, 1Y ◮ Spot exchange rates (source: Datastream / Reuters) ◮ LIBOR rates (source: Datastream / Reuters)

Foreign Exchange Options

Data

Option prices are quoted in term of the Garman-Kohlhagen (1983) implied volatilities: Ct(K, τ) = e−rd,t·τ ·

• Ft,τ · N(d1) − K · N(d2)
• Pt(K, τ)

= e−rd,t·τ ·

• K · N(−d2) − Ft,τ · N(−d1)
• at strike prices determined by the fixed option δ values:

Kδc = Ft · exp 1 2 σt(δc)2 · τ − σt(δc) · √τ · N−1 exp(rf ,t · τ) · δc

• Kδp

= Ft · exp 1 2 σt(δp)2 · τ + σt(δp) · √τ · N−1 − exp(rf ,t · τ) · δp

Foreign Exchange Options

Summary statistics (Table III)

Panel A: LIBOR and Implied Volatilities Currency rf ,t 10δp 25δp ATM 25δc 10δc AUD 0.0556 0.1239 0.1157 0.1103 0.1102 0.1138 CAD 0.0373 0.0849 0.0808 0.0785 0.0800 0.0833 CHF 0.0157 0.1083 0.1042 0.1038 0.1078 0.1145 EUR 0.0326 0.1047 0.1001 0.0987 0.1018 0.1077 GBP 0.0496 0.0909 0.0857 0.0831 0.0845 0.0887 JPY 0.0023 0.1048 0.1013 0.1041 0.1132 0.1264 NOK 0.0497 0.1146 0.1100 0.1086 0.1117 0.1177 NZD 0.0646 0.1385 0.1294 0.1234 0.1231 0.1269 SEK 0.0336 0.1146 0.1099 0.1086 0.1116 0.1175 USD 0.0368

Foreign Exchange Options

Summary statistics (Table III)

Panel B: FX Option Strike Values Moneyness

• Kδ

Ft

• Currency

10δp 25δp ATM 25δc 10δc AUD 0.9561 0.9785 1.0006 1.0222 1.0436 CAD 0.9695 0.9847 1.0003 1.0159 1.0316 CHK 0.9613 0.9804 1.0005 1.0217 1.0439 EUR 0.9626 0.9812 1.0004 1.0204 1.0412 GBP 0.9674 0.9839 1.0003 1.0168 1.0337 JPY 0.9625 0.9809 1.0005 1.0229 1.0488 NOK 0.9592 0.9794 1.0005 1.0224 1.0451 NZD 0.9511 0.9760 1.0007 1.0248 1.0487 SEK 0.9591 0.9794 1.0005 1.0225 1.0450

◮ The moneyness of constant-delta options changes with the implied volatility to

keep the probability of expiring in-the-money constant.

Foreign Exchange Options

Interpolation

The implied volatility functions are interpolated using the vanna-volga method (Castagna and Mercurio (2007)).

◮ Static hedging argument matching partial derivatives up to second order:

• 1. vega
• ∂CBS

∂σ

• ,
• 2. volga
• ∂2CBS

∂2σ

• ,
• 3. vanna
• ∂2CBS

∂σ∂St

• .

◮ The interpolated volatilities are approximately equal to:

˜ σt(K, τ) ≈ ln K2

K · ln K3 K

ln K2

K1 · ln K3 K1

· σt(K1, τ) + ln K

K1 · ln K3 K

ln K2

K1 · ln K3 K2

· σt(K2, τ) + ln K

K1 · ln K K2

ln K3

K1 · ln K3 K2

· σt(K3, τ)

◮ Implied volatilities are extrapolated by appending flat tails

Foreign Exchange Options

Implied volatility skew

Time-series means of implied volatilities by strike and interest rate regime:

◮ Blue – rf ,t < rd,t; Red – rf ,t > rd,t

Foreign Exchange Options

Extracting risk-neutral moments

Options contain forward looking information about the probability of currency crashes helping address potential peso problems:

◮ The dynamics of the risk-neutral distribution can be summarized using the

time-series of its risk-neutral moments (variance, skewness, kurtosis).

Foreign Exchange Options

Extracting risk-neutral moments

Options contain forward looking information about the probability of currency crashes helping address potential peso problems:

◮ The dynamics of the risk-neutral distribution can be summarized using the

time-series of its risk-neutral moments (variance, skewness, kurtosis).

◮ Risk-neutral moments can be computed from (Arrow (1964), Debreu (1959),

Breeden and Litzenberger (1978)): pt = exp(−rd,t · τ) · ∞ H(St+τ) · q(St+τ)dSt+τ H(St+τ) =

• ln St+τ

St n

Foreign Exchange Options

Extracting risk-neutral moments

Any payoff function H(St+τ) ∈ C2 with bounded expectation can be spanned using a continuum of OTM puts and calls (Bakshi and Madan (2000)): pt = exp(−rd,t · τ) ·

• H(S) − S · HS(S)
• + HS(S) · St +

+ ∞

S

HSS(K) · Ct(K, τ) · dK + S HSS(K) · Pt(K, τ) · dK

Risk-Neutral Moments

Volatility (Figure 6)

Time series means and standard errors AUD CAD CHF EUR GBP JPY NOK NZD SEK

• VarQ

0.1162 0.0824 0.1075 0.1027 0.0874 0.1113 0.1127 0.1297 0.1127 (0.0038) (0.0024) (0.0020) (0.0026) (0.0023) (0.0031) (0.0025) (0.0032) (0.0025) SkewQ

• 0.1941
• 0.0628

0.1105 0.0553

• 0.0562

0.4018 0.0548

• 0.2124

0.0514 (0.0162) (0.0165) (0.0142) (0.0153) (0.0171) (0.0319) (0.0139) (0.0152) (0.0136) KurtQ 3.6835 3.6223 3.6572 3.6769 3.7166 4.2188 3.6068 3.6629 3.5980 (0.0148) (0.0182) (0.0207) (0.0215) (0.0211) (0.0377) (0.0204) (0.0150) (0.0180)

Risk-Neutral Moments

Skewness (Figure 6)

Time series means and standard errors AUD CAD CHF EUR GBP JPY NOK NZD SEK

• VarQ

0.1162 0.0824 0.1075 0.1027 0.0874 0.1113 0.1127 0.1297 0.1127 (0.0038) (0.0024) (0.0020) (0.0026) (0.0023) (0.0031) (0.0025) (0.0032) (0.0025) SkewQ

• 0.1941
• 0.0628

0.1105 0.0553

• 0.0562

0.4018 0.0548

• 0.2124

0.0514 (0.0162) (0.0165) (0.0142) (0.0153) (0.0171) (0.0319) (0.0139) (0.0152) (0.0136) KurtQ 3.6835 3.6223 3.6572 3.6769 3.7166 4.2188 3.6068 3.6629 3.5980 (0.0148) (0.0182) (0.0207) (0.0215) (0.0211) (0.0377) (0.0204) (0.0150) (0.0180)

Skewness

Forecasting currency crashes (Table V)

Option-implied skewness xst rf ,t − rd,t SkewP t SkewQ t R2 R2 NFE SkewQ t+1 3.7361 0.5776 0.3198 (0.4601) SkewQ t+1 2.1440 0.4044 0.0410 (1.0279) SkewQ t+1 0.0212 0.3810 0.0032 (0.0171) SkewQ t+1 0.5865 0.5912 0.3418 (0.0293) SkewQ t+1 3.3864

• 0.1951

0.0270 0.5606 0.7628 0.6180 (0.4922) (0.5574) (0.0078) (0.0336) ◮ Potential evidence of price pressure in FX option market; consistent with

Brunnermeier, Nagel and Pedersen (2008).

◮ Majority of relation between risk-neutral skewness and the interest rate

differential is driven by the cross-section.

Skewness

Forecasting currency crashes (Table V)

Realized skewness xst rf ,t − rd,t SkewP t SkewQ t R2 R2 NFE SkewP t+1

• 2.9845

0.0522 0.0199 (0.7471) SkewP t+1

• 5.4556

0.0590 0.0269 (1.8684) SkewP t+1

• 0.0185

0.0382

• 0.0008

(0.0483) SkewP t+1

• 0.4746

0.0542 0.0220 (0.1557) SkewP t+1

• 1.2211
• 4.6725
• 0.0281
• 0.2742

0.0732 0.0416 (0.9328) (1.9204) (0.0506) (0.1597) ◮ Realized skewness, SkewP

t+1, is computed using daily returns within the month.

◮ Currencies that have relatively high interest rates or have been targets of

successful currency carry trades are more likely to crash.

◮ But ... protection is “cheap” precisely when it is most valuable.

Crash-Neutral Currency Carry Trades

Crash-neutral currency carry trades are constructed to:

• 1. Eliminate exposure to exchange rate movements beyond a pre-specified threshold;
• 2. Match the ex ante currency exposure of the standard carry trade:

◮ Necessary for expected return comparisons. ◮ Focusing on Sharpe ratios may be inappropriate due to non-linearity.

Example: AUD/USD CNCT

◮ Borrow in USD (rd,t), lend in AUD (rf ,t) ◮ Buy qp put options with a strike price of Kp on the AUD/USD exchange rate and

delta hedge the option overlay

◮ Purchase of the option overlay is financed at the domestic rate ◮ Positions established at the end of month t, and held until the end of month

t + 1 (buy-and-hold).

Crash-Neutral Currency Carry Trades

Payoff diagram (Figure 4)

The payoff to the crash-neutral currency carry trade is given by:

• CT

CN t+1(rf ,t > rd,t)

= qp · max(Kp, ˜ St+1) − exp(rd,t · τ) · ((1 − qp · δp) · St + qp · Pt(Kp, τ))

• CT

CN t+1(rd,t > rf ,t)

= exp(rd,t · τ) · ((1 + qc · δc) · St − qc · Ct(Kc, τ)) − qc · min(Kc, ˜ St+1)

Crash-Neutral Currency Carry Trades

Historical performance – portfolio strategies (Table VII)

Excess returns to the crash-neutral currency carry trade:

◮ continue to be positive and statistically significant, but; ◮ experience a statistically significant decline relative to their unhedged

counterparts that is monotonically related to the amount of protection sought.

Panel A: Non-dollar-neutral portfolios (1999:1-2007:3) CNCT(10δ) CNCT(25δ) CNCT(ATM) EQL SPR EQL SPR EQL SPR Mean 0.0459 0.0720 0.0369 0.0582 0.0193 0.0320 t-stat 3.13 3.77 2.77 3.40 1.81 2.37

• Std. dev.

0.0421 0.0549 0.0382 0.0492 0.0306 0.0387 Skewness

• 0.23
• 0.12

0.22 0.30 0.89 0.90 Kurtosis 3.51 3.04 3.37 2.90 3.63 3.42 Min

• 0.0312
• 0.0351
• 0.0290
• 0.0275
• 0.0154
• 0.0157

Max 0.0359 0.0435 0.0327 0.0398 0.0289 0.0355 SR 1.09 1.31 0.97 1.18 0.63 0.83 Mean (diff)

• 0.0101
• 0.0124
• 0.0191
• 0.0262
• 0.0367
• 0.0524

t-stat (diff)

• 4.6
• 6.23
• 3.55
• 4.66
• 3.98
• 5.02

Crash-Neutral Currency Carry Trades

Historical performance – portfolio strategies (Table VII)

Excess returns to the crash-neutral currency carry trade remain positive and statistically significant for spread-weighted strategy even after the sample is extended through Oct. 2008.

Panel A: Non-dollar-neutral portfolios (1999:1-2008:10) CNCT(10δ) CNCT(25δ) CNCT(ATM) EQL SPR EQL SPR EQL SPR Mean 0.0237 0.0432 0.0210 0.0370 0.0098 0.0190 t-stat 1.55 2.16 1.65 2.22 1.01 1.55

• Std. dev.

0.0476 0.0625 0.0398 0.0517 0.0302 0.0383 Skewness

• 0.94
• 0.82

0.01 0.04 0.90 0.91 Kurtosis 6.28 5.50 3.78 3.38 3.77 3.55 Min

• 0.0618
• 0.0763
• 0.0354
• 0.0443
• 0.0154
• 0.0198

Max 0.0805 0.0435 0.0327 0.0398 0.0289 0.0355 SR 0.50 0.69 0.53 0.72 0.32 0.50 Mean (diff)

• 0.0029
• 0.0050
• 0.0057
• 0.0111
• 0.0169
• 0.0292

t-stat (diff)

• 0.64
• 1.06
• 0.65
• 1.15
• 1.30
• 1.94

Crash-Neutral Currency Carry Trades

Total return indices

An equal-weighted portfolio of crash-neutral currency carry trades delivers statistically significant excess returns with positive skewness.

Crash-Neutral Currency Carry Trades

Historical performance – portfolio strategies (Table VII)

Excess returns to the dollar-neutral crash-neutral currency carry trade are generally indistinguishable from zero once the sample is extended through Oct. 2008.

Panel B: Dollar-neutral portfolios (1999:1-2008:10) CNCT(10δ) CNCT(25δ) CNCT(ATM) EQL SPR EQL SPR EQL SPR Mean 0.0030 0.0171 0.0051 0.0165

• 0.0056
• 0.0007

t-stat 0.14 0.61 0.30 0.72

• 0.39
• 0.04
• Std. dev.

0.0654 0.0881 0.0538 0.0714 0.0436 0.0548 Skewness

• 1.28
• 1.29
• 0.33
• 0.31

0.43 0.58 Kurtosis 7.60 8.52 3.40 4.36 2.83 3.04 Min

• 0.0944
• 0.1308
• 0.0516
• 0.0759
• 0.0239
• 0.0315

Max 0.0414 0.0624 0.0353 0.0571 0.0332 0.0469 SR 0.05 0.19 0.10 0.23

• 0.12
• 0.01

Mean (diff)

• 0.0089
• 0.0120
• 0.0068
• 0.0127
• 0.0175
• 0.0298

t-stat (diff)

• 1.32
• 1.74
• 0.48
• 0.83
• 0.82
• 1.21

Crash-Neutral Currency Carry Trades

Historical performance – portfolio strategies (Table VII)

Results are robust to hedging in fixed delta or moneyness space. The returns to crash-hedged carry trade portfolios with protection that is roughly 2.5% OTM are similar to 25δ hedging.

Constant moneyness hedging (1999:1-2008:10) CNCT(5% OTM) EQL SPR $N-EQL $N-SPR Mean 0.0221 0.0390 0.0029 0.0152 t-stat 1.71 2.32 0.17 0.67

• Std. dev.

0.0403 0.0524 0.0534 0.0709 Skewness 0.12 0.13

• 0.21
• 0.06

Kurtosis 3.20 2.91 2.79 3.44 Min

• 0.0287
• 0.0345
• 0.0399
• 0.0569

Max 0.0327 0.0408 0.0322 0.0595 SR 0.55 0.74 0.05 0.21 Mean (diff)

• 0.0045
• 0.0092
• 0.0090
• 0.0139

t-stat (diff)

• 0.51
• 0.92
• 0.65
• 0.88

Conclusions

• 1. The time-series dynamics of realized and risk-neutral skewness indicate that

protection against currency crashes is relatively cheap in periods in which it is most valuable.

• 2. At most 30-40% of the excess return stemming from exploiting UIP violations can

be attributed to exposure to currency crashes (Jan. 1999 - Mar. 2007).

• 3. In order to rationalize the entirety of the excess returns to currency carry trades

exploiting violations in UIP, would require implied volatilities on foreign exchange

• ptions to be 2-4x their actual values, indicating a massive mispricing in the

currency option market.

• 4. Asymmetry with respect to dollar exposure is an important determinant of
• performance. Spread-weighted carry trades, which are not dollar-neutral, remain

profitable even after hedging crash risk using 10δ and 25δ options.